[LDL (OP)]

My aim here is to demonstrate that if the speeds of light are affected by a gravitational field, then time dilation between two clocks or observers in relative motion will not occur.

Einstein's accelerating elevator thought experiment demonstrates light from a flashlight to bend when it travels laterally to the accelerating direction. This demonstrates that light traveling laterally in a gravitational field will fall. But what is happening to light in the upward and downward direction? It's obvious that within the upward accelerating elevator, light in the upper direction is decreasing in relative speed with the elevator while light in the downward direction increases in relative speed. The changes are balanced in that the absolute value of increase equals the absolute value of decrease.
 
It would seem then that the equivalence principle directly infers that a gravitational field is a field where the speeds of light, in line with the field, are undergoing balanced changes in opposing speeds.

A gravitational model should incorporate this principle. I present one simple model. The speeds of light around a mass should be sloped. In relation to a body of mass, the speeds of light are constant at any fixed distance but change in balance fashion in relation to the distance from the mass, c+v inbound and c-v outbound where v is the gravitational escape velocity. The rate of change of the balanced speeds of light determine the fall rate. It?s simple and intuitive. We can readily ascertain why increasing time dilation occurs the deeper a clock is placed (and prevented from falling) in a gravitational field.

Now let's picture a body where the surface speeds of light are c+v inward and c-v outward. We place a clock on the right side of the body and it runs at a certain rate of time based on those speeds.

Let's choose three different locations within a section of space, from left to right, C, B and A, equal distance apart in a linear arrangement. If we place the body stationary at location A, we observe the speeds of light to the right of the body to be c+v left and c-v right. If we place the body at position B, the same light speeds are observed but in a further left location. And of course the c+v and c-v speeds are even further left when the body is placed at position C.

Now let's put the body in motion left at speed s traveling through A,B and C. A stationary observer would see the speeds of light to be c+v left and c-v right near location A, then disappear and reappear at location B, then disappear again and reappear at location C. Even though the stationary observer never observes the speeds of light to actually travel any difference in speed, the disappearing and reappearing at a further location creates a wave like motion of these speeds. Note the faster the body moves left the more space between the appearing c+v and c-v speeds. This is a red shift of a wave. Let's define these speeds by vectors. The speed vectors, representing c+v left and c-v right, are moving left at speed s keeping in sync with the moving body and maintaining the speed relationships of the two-way speeds of light near the surface of the moving body. No matter what speed the body travels at, the vectors will follow and maintain this relationship. The rate of time of the clock on the right side of the body will be the same for any speed the body travels at. No dilation of time occurs.

We can consider small body's where the changes in the sloped fields are negligible, where surface speeds of c+v in and c-v out are very close to c in and c out, though there must still be a small gradient of slope.

If we place this body at position A, light in and light out both have the speed of c. When the body is placed at position B, its light in and light out is also c. And we obtain the same result when the body is placed at position C.
When the body is given a constant speed traveling though A, B and C, all emitted and incoming light is swept by a wave. The speed vectors on the right side of the body representing c left and c right, are moving left at speed s keeping in sync with the moving body and maintaining the speed relationships with the moving body and maintaining its rate of time. From the point of view of the other body our speeds are also in sync with our relative motion and light is emitted and received at speed c.

Approaching light from a body that is moving away, is pulled forward by our gravitational field to increase its speed relative to the moving source and stretched causing red shifting of its wave. Red shifted light moves faster than c relative to its source. Approaching light from a body moving toward us, is pushed back by our gravitational field to lower its speed relative to the moving source and compressed causing blue shifting. Blue shifted light moves slower than c relative to its source. The rate of time for both receiver and emitter of light remains constant in all cases.

With this model we can eliminate all the confounding oddities that infiltrate relativity theory. No differences in rates of time between bodies in relative motion, no Twin paradox, no absurd notion that two bodies in relative motion each see the other running at a slower rate of time, no length contraction, and of course, no curved space-time.

It's just that the sloped speeds of light are a consequence of a gravitational field and the gravitational field keeps in sync with a uniform moving mass just like field lines around uniform moving charges.

[Kryptid]

We have experiments showing that time does indeed slow for observers in relative motion, so any conclusions you draw must take that into consideration.

[LDL (OP)]

I question time dilation occurs in relative motion in absence of mechanical type forces.
Time dilation occurs within a time clock when the internal beam spends more time in one direction then the other. I call this time shifting.
Prevention from falling (which requires a force) creates direct time shifting because the two-way speeds of light differ. The further away from the surface of a mass the less time shifting occurs.
Particle accelerators create acceleration. Is it differentiated that dilation is a result of the speed and not the acceleration?
Do Muons traveling thru an atmosphere not encounter frictional forces.
Do orbiting clocks undergo centripetal acceleration.

[Eternal Student]

Hi.

      Your article is well written but it seems to be suggesting a logical connection from one thing to another that actually isn't as obvious as you imply.

    If I've understood what you've said,   you are proposing the following:

I present one simple model. The speeds of light around a mass should be sloped. In relation to a body of mass, the speeds of light are constant at any fixed distance but change in balance fashion in relation to the distance from the mass, c+v inbound and c-v outbound where v is the gravitational escape velocity.

    That seems as if you were considering the speeds of light in a frame of reference where the mass (e.g. a planet) can be taken as being stationary.   For example, we could have the mass at the origin at all times.
    You don't seem to have any experimental evidence that you've presented but there is a general implication that your earlier example involving an elevator provides some motivation for it.

      Unfortunately, your previous elevator example is different:    In that example, it seems as if you would be using a frame of reference where the centre of the elevator is always at the origin,   so that's an accelerated frame.    The nearest equivalent frame for light around the mass would then also be an accelerated frame,  e.g. one that is in free-fall toward the planet rather than always having the planet at the origin.   Moreover, since you talk about increasing the distance from the planet, you couldn't even use just the one frame all the time,   at every new disatnce there is a different gravitational acceleration toward the planet, so the free-fall frame would be different.

      Therefore, the elevator example doesn't really provide the motivation or justification for your proposal that you might have thought.

    To say this a different way:   You have something that will hold in one sort of frame but then you overlook the type of frame it was and tacitly assume it can apply to any old frame we wish.

- - - - - - - - - - -
      Under the mainstream theory of Relativity, the speed of light CAN be different in an accelerated frame of reference.    So your elevator example isn't necessarily wrong.   I'm not saying that your proposal is wrong only that it doesn't follow logically (because you start using different sorts of frames) and you would want some evidence for it.

Best Wishes.

[LDL (OP)]

Whatever gravitational model you want, my main point here is that if a gravitational field governs the speeds of light, it governs the rate of time.

Picture a body moving away. This body is surrounded by a gravitational field. Picture inward pointing field lines just like in uniform moving charges. Those field lines represent the speeds of light and they stay in sync with the moving body no matter what speed the body is traveling.

We can now say that the speeds of light are constant in all inertial frame of reference and understand why. But to communicate with bodies in relative motion, incoming light is altered in speed by our field and we see this alteration by the red or blue shifting of the incoming light wave.

No time dilation for either.

Otherwise think of what relativity is saying

You view a body moving away and it looks to you that the body has changed its relation to the two-way speed of light  (which is dictated by your field) and it must have its time dilated.

But you are also told that from the moving body's point of view, it views your rate of time to have slowed within its field.

Both viewpoints can't be right.

You explain this away in that It depends on how they got there and if they come back to their original location. But if they don't meet again, we cannot determine who is aging faster.

So let's look at A and B a certain distance apart and push B into A.

A sees B in motion and determines that B is in motion within its field and thereby concludes that B's rate of time to be slower. A says that its field determines the rate of time for B.

But B says from my viewpoint A is in my field and my field determines that A's rate of time is running slower.

But A says to B, no you do not have a field. When you were pushed into my field your field did not come with you.

I beg to differ; says B. My field is right here with me. It came along with me when I was pushed. It's attached to me and I can't get rid of it.

[LDL (OP)]

One last point I would like to make before this post is ended. It involves the significance of the push. Two bodies or observers A and B with clocks a certain distance apart can synchronize their time, when not in relative motion. They are in the same inertial frame of reference. A can send a light beam to B and back and determine the distance, then send another beam that will start B's clock. A can calculate the time it would take for the second beam to reach B and start his own clock accordingly. Their clocks are now synchronized.

According to relativity, If we apply  an application of force to B, a push say, B will be put in motion towards A. When B reaches A, they collide which immediately freezes the clocks. We should then find that B's time is behind A's. Its rate of time was decreased during the excursion towards A.

I find this somewhat defies the principle of relative motion where there should be an absence of a frame of reference or an aether.

I imagine myself to be B. I feel the push and immediately after I see that A is coming towards me. But I studied relativity and I know this not the case. I know my time is running slower than A's. I am moving through A's inertial frame of reference. Let's call an inertial frame of reference a field.

I am moving through A's field. I am moving through an aether of sorts. My rate of time is determined by my motion through A's field. Please don't tell me that the speeds of light around me are c in and c out. They cannot be. They must be c+v in and c-v out. How else will my rate of time decrease if that isn't the case.

I've somehow lost my own field. All because I was pushed. If A had been pushed then I would retain my field and A's rate of time would be determined by how it moves through my field.

So there are many bodies in relative motion. How do we know which field affects which bodies. We would have to know the history of how they all got to where they are.

But perhaps a field cannot be lost. Maybe a gravitational field, which, every body has, maintains the speed of light to be stringently c. Motion through other fields then can't influence it. But then you would not have time dilation in relative motion